lib/intprops.h

   1 /* intprops.h -- properties of integer types
   2
   3    Copyright (C) 2001-2017 Free Software Foundation, Inc.
   4
   5    This program is free software: you can redistribute it and/or modify it
   6    under the terms of the GNU General Public License as published
   7    by the Free Software Foundation; either version 3 of the License, or
   8    (at your option) any later version.
   9
  10    This program is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13    GNU General Public License for more details.
  14
  15    You should have received a copy of the GNU General Public License
  16    along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
  17
  18 /* Written by Paul Eggert.  */
  19
  20 #ifndef _GL_INTPROPS_H
  21 #define _GL_INTPROPS_H
  22
  23 #include <limits.h>
  24
  25 /* Return a value with the common real type of E and V and the value of V.  */
  26 #define _GL_INT_CONVERT(e, v) (0 * (e) + (v))
  27
  28 /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
  29    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>.  */
  30 #define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))
  31
  32 /* The extra casts in the following macros work around compiler bugs,
  33    e.g., in Cray C 5.0.3.0.  */
  34
  35 /* True if the arithmetic type T is an integer type.  bool counts as
  36    an integer.  */
  37 #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
  38
  39 /* True if the real type T is signed.  */
  40 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
  41
  42 /* Return 1 if the real expression E, after promotion, has a
  43    signed or floating type.  */
  44 #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
  45
  46
  47 /* Minimum and maximum values for integer types and expressions.  */
  48
  49 /* The width in bits of the integer type or expression T.
  50    Padding bits are not supported; this is checked at compile-time below.  */
  51 #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
  52
  53 /* The maximum and minimum values for the integer type T.  */
  54 #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
  55 #define TYPE_MAXIMUM(t)                                                 \
  56   ((t) (! TYPE_SIGNED (t)                                               \
  57         ? (t) -1                                                        \
  58         : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
  59
  60 /* The maximum and minimum values for the type of the expression E,
  61    after integer promotion.  E should not have side effects.  */
  62 #define _GL_INT_MINIMUM(e)                                              \
  63   (EXPR_SIGNED (e)                                                      \
  64    ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \
  65    : _GL_INT_CONVERT (e, 0))
  66 #define _GL_INT_MAXIMUM(e)                                              \
  67   (EXPR_SIGNED (e)                                                      \
  68    ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
  69    : _GL_INT_NEGATE_CONVERT (e, 1))
  70 #define _GL_SIGNED_INT_MAXIMUM(e)                                       \
  71   (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
  72
  73 /* Work around OpenVMS incompatibility with C99.  */
  74 #if !defined LLONG_MAX && defined __INT64_MAX
  75 # define LLONG_MAX __INT64_MAX
  76 # define LLONG_MIN __INT64_MIN
  77 #endif
  78
  79 /* This include file assumes that signed types are two's complement without
  80    padding bits; the above macros have undefined behavior otherwise.
  81    If this is a problem for you, please let us know how to fix it for your host.
  82    This assumption is tested by the intprops-tests module.  */
  83
  84 /* Does the __typeof__ keyword work?  This could be done by
  85    'configure', but for now it's easier to do it by hand.  */
  86 #if (2 <= __GNUC__ \
  87      || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
  88      || (0x5110 <= __SUNPRO_C && !__STDC__))
  89 # define _GL_HAVE___TYPEOF__ 1
  90 #else
  91 # define _GL_HAVE___TYPEOF__ 0
  92 #endif
  93
  94 /* Return 1 if the integer type or expression T might be signed.  Return 0
  95    if it is definitely unsigned.  This macro does not evaluate its argument,
  96    and expands to an integer constant expression.  */
  97 #if _GL_HAVE___TYPEOF__
  98 # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
  99 #else
 100 # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
 101 #endif
 102
 103 /* Bound on length of the string representing an unsigned integer
 104    value representable in B bits.  log10 (2.0) < 146/485.  The
 105    smallest value of B where this bound is not tight is 2621.  */
 106 #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
 107
 108 /* Bound on length of the string representing an integer type or expression T.
 109    Subtract 1 for the sign bit if T is signed, and then add 1 more for
 110    a minus sign if needed.
 111
 112    Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
 113    signed, this macro may overestimate the true bound by one byte when
 114    applied to unsigned types of size 2, 4, 16, ... bytes.  */
 115 #define INT_STRLEN_BOUND(t)                                     \
 116   (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
 117    + _GL_SIGNED_TYPE_OR_EXPR (t))
 118
 119 /* Bound on buffer size needed to represent an integer type or expression T,
 120    including the terminating null.  */
 121 #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
 122
 123
 124 /* Range overflow checks.
 125
 126    The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
 127    operators might not yield numerically correct answers due to
 128    arithmetic overflow.  They do not rely on undefined or
 129    implementation-defined behavior.  Their implementations are simple
 130    and straightforward, but they are a bit harder to use than the
 131    INT_<op>_OVERFLOW macros described below.
 132
 133    Example usage:
 134
 135      long int i = ...;
 136      long int j = ...;
 137      if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
 138        printf ("multiply would overflow");
 139      else
 140        printf ("product is %ld", i * j);
 141
 142    Restrictions on *_RANGE_OVERFLOW macros:
 143
 144    These macros do not check for all possible numerical problems or
 145    undefined or unspecified behavior: they do not check for division
 146    by zero, for bad shift counts, or for shifting negative numbers.
 147
 148    These macros may evaluate their arguments zero or multiple times,
 149    so the arguments should not have side effects.  The arithmetic
 150    arguments (including the MIN and MAX arguments) must be of the same
 151    integer type after the usual arithmetic conversions, and the type
 152    must have minimum value MIN and maximum MAX.  Unsigned types should
 153    use a zero MIN of the proper type.
 154
 155    These macros are tuned for constant MIN and MAX.  For commutative
 156    operations such as A + B, they are also tuned for constant B.  */
 157
 158 /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
 159    See above for restrictions.  */
 160 #define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \
 161   ((b) < 0                                              \
 162    ? (a) < (min) - (b)                                  \
 163    : (max) - (b) < (a))
 164
 165 /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
 166    See above for restrictions.  */
 167 #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \
 168   ((b) < 0                                              \
 169    ? (max) + (b) < (a)                                  \
 170    : (a) < (min) + (b))
 171
 172 /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
 173    See above for restrictions.  */
 174 #define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \
 175   ((min) < 0                                            \
 176    ? (a) < - (max)                                      \
 177    : 0 < (a))
 178
 179 /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
 180    See above for restrictions.  Avoid && and || as they tickle
 181    bugs in Sun C 5.11 2010/08/13 and other compilers; see
 182    <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */
 183 #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \
 184   ((b) < 0                                              \
 185    ? ((a) < 0                                           \
 186       ? (a) < (max) / (b)                               \
 187       : (b) == -1                                       \
 188       ? 0                                               \
 189       : (min) / (b) < (a))                              \
 190    : (b) == 0                                           \
 191    ? 0                                                  \
 192    : ((a) < 0                                           \
 193       ? (a) < (min) / (b)                               \
 194       : (max) / (b) < (a)))
 195
 196 /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
 197    See above for restrictions.  Do not check for division by zero.  */
 198 #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \
 199   ((min) < 0 && (b) == -1 && (a) < - (max))
 200
 201 /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
 202    See above for restrictions.  Do not check for division by zero.
 203    Mathematically, % should never overflow, but on x86-like hosts
 204    INT_MIN % -1 traps, and the C standard permits this, so treat this
 205    as an overflow too.  */
 206 #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \
 207   INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
 208
 209 /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
 210    See above for restrictions.  Here, MIN and MAX are for A only, and B need
 211    not be of the same type as the other arguments.  The C standard says that
 212    behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
 213    A is negative then A << B has undefined behavior and A >> B has
 214    implementation-defined behavior, but do not check these other
 215    restrictions.  */
 216 #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \
 217   ((a) < 0                                              \
 218    ? (a) < (min) >> (b)                                 \
 219    : (max) >> (b) < (a))
 220
 221 /* True if __builtin_add_overflow (A, B, P) works when P is non-null.  */
 222 #if 5 <= __GNUC__ && !defined __ICC
 223 # define _GL_HAS_BUILTIN_OVERFLOW 1
 224 #else
 225 # define _GL_HAS_BUILTIN_OVERFLOW 0
 226 #endif
 227
 228 /* True if __builtin_add_overflow_p (A, B, C) works.  */
 229 #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
 230
 231 /* The _GL*_OVERFLOW macros have the same restrictions as the
 232    *_RANGE_OVERFLOW macros, except that they do not assume that operands
 233    (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume
 234    that the result (e.g., A + B) has that type.  */
 235 #if _GL_HAS_BUILTIN_OVERFLOW_P
 236 # define _GL_ADD_OVERFLOW(a, b, min, max)                               \
 237    __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
 238 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \
 239    __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
 240 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \
 241    __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
 242 #else
 243 # define _GL_ADD_OVERFLOW(a, b, min, max)                                \
 244    ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \
 245     : (a) < 0 ? (b) <= (a) + (b)                                         \
 246     : (b) < 0 ? (a) <= (a) + (b)                                         \
 247     : (a) + (b) < (b))
 248 # define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \
 249    ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \
 250     : (a) < 0 ? 1                                                        \
 251     : (b) < 0 ? (a) - (b) <= (a)                                         \
 252     : (a) < (b))
 253 # define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \
 254    (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
 255     || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
 256 #endif
 257 #define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \
 258   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 259    : (a) < 0 ? (b) <= (a) + (b) - 1                                     \
 260    : (b) < 0 && (a) + (b) <= (a))
 261 #define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \
 262   ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \
 263    : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \
 264    : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
 265
 266 /* Return a nonzero value if A is a mathematical multiple of B, where
 267    A is unsigned, B is negative, and MAX is the maximum value of A's
 268    type.  A's type must be the same as (A % B)'s type.  Normally (A %
 269    -B == 0) suffices, but things get tricky if -B would overflow.  */
 270 #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \
 271   (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \
 272     ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \
 273        ? (a)                                                            \
 274        : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \
 275     : (a) % - (b))                                                      \
 276    == 0)
 277
 278 /* Check for integer overflow, and report low order bits of answer.
 279
 280    The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
 281    might not yield numerically correct answers due to arithmetic overflow.
 282    The INT_<op>_WRAPV macros also store the low-order bits of the answer.
 283    These macros work correctly on all known practical hosts, and do not rely
 284    on undefined behavior due to signed arithmetic overflow.
 285
 286    Example usage, assuming A and B are long int:
 287
 288      if (INT_MULTIPLY_OVERFLOW (a, b))
 289        printf ("result would overflow\n");
 290      else
 291        printf ("result is %ld (no overflow)\n", a * b);
 292
 293    Example usage with WRAPV flavor:
 294
 295      long int result;
 296      bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
 297      printf ("result is %ld (%s)\n", result,
 298              overflow ? "after overflow" : "no overflow");
 299
 300    Restrictions on these macros:
 301
 302    These macros do not check for all possible numerical problems or
 303    undefined or unspecified behavior: they do not check for division
 304    by zero, for bad shift counts, or for shifting negative numbers.
 305
 306    These macros may evaluate their arguments zero or multiple times, so the
 307    arguments should not have side effects.
 308
 309    The WRAPV macros are not constant expressions.  They support only
 310    +, binary -, and *.  The result type must be signed.
 311
 312    These macros are tuned for their last argument being a constant.
 313
 314    Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
 315    A % B, and A << B would overflow, respectively.  */
 316
 317 #define INT_ADD_OVERFLOW(a, b) \
 318   _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
 319 #define INT_SUBTRACT_OVERFLOW(a, b) \
 320   _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
 321 #if _GL_HAS_BUILTIN_OVERFLOW_P
 322 # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
 323 #else
 324 # define INT_NEGATE_OVERFLOW(a) \
 325    INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 326 #endif
 327 #define INT_MULTIPLY_OVERFLOW(a, b) \
 328   _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
 329 #define INT_DIVIDE_OVERFLOW(a, b) \
 330   _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
 331 #define INT_REMAINDER_OVERFLOW(a, b) \
 332   _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
 333 #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
 334   INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
 335                                  _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
 336
 337 /* Return 1 if the expression A <op> B would overflow,
 338    where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
 339    assuming MIN and MAX are the minimum and maximum for the result type.
 340    Arguments should be free of side effects.  */
 341 #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
 342   op_result_overflow (a, b,                                     \
 343                       _GL_INT_MINIMUM (0 * (b) + (a)),          \
 344                       _GL_INT_MAXIMUM (0 * (b) + (a)))
 345
 346 /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
 347    Return 1 if the result overflows.  See above for restrictions.  */
 348 #define INT_ADD_WRAPV(a, b, r) \
 349   _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
 350 #define INT_SUBTRACT_WRAPV(a, b, r) \
 351   _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
 352 #define INT_MULTIPLY_WRAPV(a, b, r) \
 353   _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
 354
 355 /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:
 356    https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
 357    https://llvm.org/bugs/show_bug.cgi?id=25390
 358    For now, assume all versions of GCC-like compilers generate bogus
 359    warnings for _Generic.  This matters only for older compilers that
 360    lack __builtin_add_overflow.  */
 361 #if __GNUC__
 362 # define _GL__GENERIC_BOGUS 1
 363 #else
 364 # define _GL__GENERIC_BOGUS 0
 365 #endif
 366
 367 /* Store the low-order bits of A <op> B into *R, where OP specifies
 368    the operation.  BUILTIN is the builtin operation, and OVERFLOW the
 369    overflow predicate.  Return 1 if the result overflows.  See above
 370    for restrictions.  */
 371 #if _GL_HAS_BUILTIN_OVERFLOW
 372 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
 373 #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
 374 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 375    (_Generic \
 376     (*(r), \
 377      signed char: \
 378        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 379                         signed char, SCHAR_MIN, SCHAR_MAX), \
 380      short int: \
 381        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 382                         short int, SHRT_MIN, SHRT_MAX), \
 383      int: \
 384        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 385                         int, INT_MIN, INT_MAX), \
 386      long int: \
 387        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 388                         long int, LONG_MIN, LONG_MAX), \
 389      long long int: \
 390        _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 391                         long long int, LLONG_MIN, LLONG_MAX)))
 392 #else
 393 # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
 394    (sizeof *(r) == sizeof (signed char) \
 395     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 396                        signed char, SCHAR_MIN, SCHAR_MAX) \
 397     : sizeof *(r) == sizeof (short int) \
 398     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 399                        short int, SHRT_MIN, SHRT_MAX) \
 400     : sizeof *(r) == sizeof (int) \
 401     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
 402                        int, INT_MIN, INT_MAX) \
 403     : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
 404 # ifdef LLONG_MAX
 405 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 406     (sizeof *(r) == sizeof (long int) \
 407      ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 408                         long int, LONG_MIN, LONG_MAX) \
 409      : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
 410                         long long int, LLONG_MIN, LLONG_MAX))
 411 # else
 412 #  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
 413     _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
 414                      long int, LONG_MIN, LONG_MAX)
 415 # endif
 416 #endif
 417
 418 /* Store the low-order bits of A <op> B into *R, where the operation
 419    is given by OP.  Use the unsigned type UT for calculation to avoid
 420    overflow problems.  *R's type is T, with extrema TMIN and TMAX.
 421    T must be a signed integer type.  Return 1 if the result overflows.  */
 422 #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
 423   (sizeof ((a) op (b)) < sizeof (t) \
 424    ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
 425    : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
 426 #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
 427   ((overflow (a, b) \
 428     || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
 429     || (tmax) < ((a) op (b))) \
 430    ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
 431    : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
 432
 433 /* Return the low-order bits of A <op> B, where the operation is given
 434    by OP.  Use the unsigned type UT for calculation to avoid undefined
 435    behavior on signed integer overflow, and convert the result to type T.
 436    UT is at least as wide as T and is no narrower than unsigned int,
 437    T is two's complement, and there is no padding or trap representations.
 438    Assume that converting UT to T yields the low-order bits, as is
 439    done in all known two's-complement C compilers.  E.g., see:
 440    https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
 441
 442    According to the C standard, converting UT to T yields an
 443    implementation-defined result or signal for values outside T's
 444    range.  However, code that works around this theoretical problem
 445    runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:
 446    http://lists.gnu.org/archive/html/bug-gnulib/2017-04/msg00049.html
 447    As the compiler bug is real, don't try to work around the
 448    theoretical problem.  */
 449
 450 #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
 451   ((t) ((ut) (a) op (ut) (b)))
 452
 453 #endif /* _GL_INTPROPS_H */